internal number representation

[jte]

Two key differences between HP_Real and IEEE 754/854 formats is that HP_Real doesn't have signed zeroes and doesn't have denormalized numbers (no gradual underflow).

The 15-digit HP_Real can be used for internal calculations: to provide guard digits and to simulate gradual underflow of 12-digit HP_Real values, among other uses. The greater exponent range allows things like more direct calculation of sqrt(x^2+y^2) — by using 15-digit HP_Reals for the operations even though x and y are 12-digit HP_Real values.

The two systems also have different rounding behaviours.

NaNs are also treated differently (especially when used via PPL).